higher order terms in quadrupoles

[eadli]

I am questioning what the higher order terms consist of when asking for higher order terms in a quadrupole. E.g. by setting: quad, order=4.

I would expect the expansion to be only in energy, while the quad remained perfectly linear in the transverse.

However, using the following test case, this seems not to be the case. My test case is a simple lattice with two quads (modelled with quad, order=2 and quad,order=4 respectivly), set to imaging condition m34=0. I send in a test beam where all particles have constant energy (energy imaged) and only differ by their initial y'. When I turn on higher order in the quad (or use kquad), the imaging is no longer preserved. See this view-graph:
https://www.dropbox.com/s/phoysjar0kyxc ... oblems.pdf

Since there is not a lot of information in the manual, it would be helpful if someone could elucidate how the higher order expansion works.

Thank you, Erik

[michael_borland]

Erik,

Sorry that the manual doesn't have any detail on this. As you might imagine, the third-order matrix for a quad is rather complicated and not easy to document.

The third order terms probably result from the combination of first-order deflection and second-order path-lengthening (Sqrt[1 + (xp^2+yp^2)]). You can test this hypothesis by using a very short magnet.

Note that KQUAD and QUAD are implemented in completely different ways: KQUAD uses symplectic integration of the exact Hamiltonian using a 4th-order Ruth integrator. QUAD uses a transport matrix (up to 3rd order) using analytical expressions derived with mathematica.

--Michael